2 Performance Considerations
The program does not take into account the existence of the AMS magnetic field. The z position of the top of the support structure, holding both layers of aerogel, was assumed to be at -98 cm from the start of the AMS coordinate system. A simplified tracker acceptance was used in the calculation. The tracker was defined as having a radius, R=52.5 cm, with two layers (number two and five of silicon) placed at z2=32 cm, and z5=-32 cm (AMS coordinates). Furthermore, the tracker acceptance in Y is reduced by a cut: 
cm. In this calculation we are interested to see the effect that the geometric acceptance of the ATC will have on the rejection power. The tracking step in the aerogel volume was taken to be 1 mm. We have assumed three levels of electronics sensitivity: 1, 2, or 3 photoelectrons cut. It is obvious that the more sensitive (and less noisy) the readout electronics the more performant the ATC will be. The rejection power of the detector increases significantly if the two layers are displaced by half-cell length on each x, y direction. This way the effects of gaps are reduced dramatically. A summary of the results is given in table 2-5.
The calculations indicate that we gain a factor two in rejection, by displacing the two layers of aerogel by 5.5 cm on each axis. Furthermore, gaps on the Y-axis (i.e. along the X-axis) are more important than gaps along the X-axis. This is due to the acceptance of the tracker which is not the same along the two axes. Since aerogel will be wrapped in PTFE (0.75 mm thick on each side) the minimum gap between blocks is 1.5 mm (2x0.75 mm). Assuming selection or cutting (Section 3.5) we can keep close to this requirement. In any case, assuming a careful construction of the detector, with gap tolerances less than 1 mm we can conclude that the rejection power of ATC will be sufficient given the expected electron background. In addition, we have studied the possibility of making two of the walls thicker by 2 mm, per layer, in order to improve the rigidity of the structure. Assuming one photoelectron sensitivity and selected/cut blocks (i.e. x, y gaps = 0.15 cm), the rejection power remains satisfactory: Rejection = 7600. Assuming a 0.1 cm tolerance in the dimensions of the blocks (i.e. x, y gaps = 0.25 cm), Rejection = 4200, and for x, y gaps = 0.35 cm the rejection power drops to 2800. Therefore, the tolerances of the blocks must be kept at a minimum by careful selection and/or cutting of the blocks, and the electronics sensitivity of the detector must be at the single photoelectron level.